"If this wasn't an internet bank it would be the equivalent of a High Street bank closing some of its branches.

"It's been shut for four days but they advertise my money as being on instant demand," he added.

The bank's website carries an apology to customers.

"We want to apologise unreservedly to our savings customers who have experienced difficulties in accessing our online banking system in recent days," the message on the Tesco website says.

I am at boiling point. I have no access to my accountJohan Sinclair, Tesco Bank customer

"The problem has led to an increase in call volumes to our call centre and we have not been able to answer calls as quickly as you would expect, or we would like.

"The majority of customers are able to access their accounts. However, we know there are some customers that have not been able to log in," the message adds.

'At boiling point'

The bank's website carries advice on what customers should do, especially if they use the Internet Explorer 9 web browser, which was launched earlier this year.

Tesco believes that this has a compatibility problem with its system, which can be very easily fixed if customers follow some instructions to re-set their browsers.

Many customers have been frustrated at both the computer lock-out and the inability of Tesco's call centre to deal with the big jump in calls.

"I spent four hours Tuesday 21st and a further three hours so far [on Wednesday] trying to contact their helpdesk - suffering the exasperation of a disembodied voice telling me how important my call is to them, so I don't believe the issue has been fixed," Johan Sinclair told the BBC on Wednesday.

"I am at boiling point as I have no other way to contact them and in the meantime I have no access to my account."

Another BBC reader, Brian from Christchurch in Dorset, said: "This is a compete shambles, the worst episode I have come across in 15 years of using websites.

"I am still waiting for a new PIN number to come in the post, then I will have to ring them up, and go through the process of logging on again."